A warning that as many as 1,200 could face the axe as the authority struggles to balance its books comes ahead of a demonstration planned for Neath town centre on Saturday.
However, council chief executive Steve Phillips labelled Unison's assertions as "mainly wrong".
He added: "We don't recognise its numbers and would ask the union to explain them."
Unison regional organiser, Eddie Gabrielsen, told the Post that the plan to cut 750 jobs to make savings of £17 million doesn't add up.
"The proposal to cut 750 jobs is based on a calculation of 750 full-time jobs at a salary of £25,000 each," he said.
"As many jobs are part-time and earn less, in reality this is more likely to be, in the trade union's estimate, 1,200 jobs."
He said 250 job cuts had already been earmarked by the council in areas including older people's services, housing, trading standards, domicillary services, school meals, cleaning, and clerical and administration, among other departments.
Responding to the chief executive's comments about fears the job losses could be more than originally thought, Mr Gabrielsen said: "They should go back and check their figures.
"The council knows that some people are going to be earning less than £25,000 and some are going to be earning more."
A demonstration over job cuts and other issues, including the closure of seven residential care homes and fears about the privatisation of services, will take place on Saturday.
Mr Gabrielsen said the union was calling for as many people as possible to turn up and show their support for workers.
Demonstrators will meet at 10am at Milland Road car park, and will then march to Neath Civic Centre, where a rally is set to take place.
emma.denholm@swwmedia.co.uk